Convergence of martingale and moderate deviations for a branching random walk with a random environment in time

Xiaoqiang Wang, Chunmao Huang

We consider a branching random walk on $\mathbb{R}$ with a stationary and ergodic environment $\xi =({\xi }_n)$ indexed by time $n\in \mathbb{N}$. Let $Z_n$ be the counting measure of parti…